Can I replace the battery on my Apple remote. It will not recharge.

If you tried to recharge exactly as Apple intended (to a computer, or to a USB power adapter),

Charge the Siri Remote - Apple Support

then there is possibly an issue with the battery. Apple has a service for batteries that will no longer keep charge as they used to. See: Apple TV repair and service - Apple Support

Your profile indicates you have the Apple TV 4K. If that’s the case then your remote has a rechargeable battery that is not user replaceable. The cost to replace it would likely be close to the cost of a new one so…

But have you tried a different cable and/or a different charging unit? Have you taken a look at the charging port on the remote and looked for an obstruction like a pice of dirt or lint in there? Maybe try using a can of air and blowing out the port?